A bidendriform automorphism of WQSym

Abstract: By Foissy's work, the bidendriform structure of the Word Quasisymmetric Functions Hopf algebra (WQSym) implies that it is isomorphic to its dual. In this talk, we present the construction of an explicit combinatorial bidendriform isomorphism. We represent two recursive decompositions of packed words by two new combinatorial families called red and blue biplan forests. We then obtain two bases of WQSym and its dual. The advantage of these bases is that by taking explicit subsets, we obtain bases of primitive elements and totally primitive elements. We then carefully combine red and blue forests to get bicolors forests. A simple re-coloring of the edges allows us to obtain the first explicit bidendriform automorphism of WQSym.

combinatorics

Audience: researchers in the topic

York University Applied Algebra Seminar